Teleporting an Unknown Quantum State
Via Dual Classical and Einstein‐Podolsky‐Rosen Channels*
Introduction
Mohammed Sheikh, Charles Steiner, Apoorv Tiwari, Chi Hang Boyce Tsang
Department of Physics, University of Illinois at Urbana-Champaign
Goals/Motivation
Teleportation Procedure
•Teleport a quantum particle using quantum entanglement.
Source of maximally entangled
particle pairs A B
What does „teleporting‟ mean?
Alice want to send Bob a particle. However she does
not know anything about the state of the particle and
cannot give it to Bob physically. Let the particle be in
the state 𝜑 . How does Bob obtain a particle in the
exact same state 𝜑 without what it is?
1
1
2
0 𝐴⨂ 1
+
1
⨂
0
𝐵
𝐴
𝐵
Entangled state
Measuring A to be 0 means B is 1
The problem of measurement
What happens when I change my basis?
Bell basis
• Broadcasts of states in quantum mechanics are forbidden as
they require cloning
• In this procedure, Alice need no information on the location of
Bob, as classical message can be cloned and broadcasted
Quantum broadcasting
(Forbidden by quantum mechanics)
Broadcast using both
Classical and EPR channels
Bob
Bob
B
A
Alice can use quantum entanglement to
teleport a particle
When two particles interact, their
wavefunctions become
entangled if measurement of one
particle determines the state of
the other particle.
“Pseudo-broadcast” of quantum states
• Goal: Teleport state 𝜑 from particle 1 to Bob
•Understand the properties of quantum information.
Possible Implications
Alice
𝝋 Alice
𝑼 𝝋 ⨂ 𝑨 Alice
Entangle particle 1 and particle A
Apply unitary transformation
on (1,A) pair
1
Bob
A
Measure and collapse the
(1,A) entangled pair
(and hence change the
state of B)
Send the result of
measurement to Bob
with classical
channel
: EPR Channel
: Classical Channel
: Cloning (Forbidden)
: Broadcast
Wait for Alice’s
result
B
B
Apply unitary
transformation
(based on message
from Alice) on
particle B
B
with state 𝜑
: Measurement
: Broadcast
R : Result (Classical Message)
: Cloning (Allowed)
Improved Quantum Cryptography
• In this procedure, direct transfer of quantum state was avoided
• By comparing some part of the message (substring) in public,
Alice and Bob could detect eavesdropper easily
Without eavesdropper
With eavesdropper
Alice 100110011101…
100110011101…
Bob
010101011010…
100110011101…
• When Alice and Bob compare the red segment in public in the
second case, the discrepancy indicates presence of eavesdropper
Acknowledgments
Prof. Charles H. Bennett, Gilles Brassard, Claude Crépeau, Richard
Jozsa, Asher Peres, and William K. Wootters
*C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).